A steady force of $120\ N$ is required to push a boat of mass $700\ kg$ through water at a constant speed of $1\ m/s$ . If the boat is fastened by a spring and held at $2\ m$ from the equilibrium position by a force of $450\ N$ , find the angular frequency of damped $SHM$ ..... $rad/s$
$0.56$
$0.21$
$1.35$
Motion is overdamped
A mass attached to a spring is free to oscillate, with angular velocity $\omega,$ in a hortzontal plane without friction or damping. It is pulled to a distance $x_{0}$ and pushed towards the centre with a velocity $v_{ o }$ at time $t=0 .$ Determine the amplitude of the resulting oscillations in terms of the parameters $\omega, x_{0}$ and $v_{ o } .$ [Hint: Start with the equation $x=a \cos (\omega t+\theta)$ and note that the initial velocity is negative.]
A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs of equal spring constants $k$. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $\theta$ in one direction and released. The frequency of oscillation is
If a body of mass $0.98\, kg$ is made to oscillate on a spring of force constant $4.84\, N/m$, the angular frequency of the body is ..... $ rad/s$
The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended , the period of oscillation will now be
Define simple pendulum and the length of pendulum.